April 04, 2006

Cosmological Constant and the String Landscape at Solvay 2005

This is a rapporteur's talk at the 23rd Solvay Conference by Joe Polchinski, the article is dated March 31, 2006. (I feel it is the best paper of the year until now.) The author divides theories of the cosmological constant (CC) into two groups: value fixed by theory and value adjustable like in string theory landscape. The central issue in the report is to discuss the extent to which physics is predictable. Polchinski sees three major questions in the CC: why it is not large, not zero, but comparable to the matter density now. He focuses mainly in the first question: "this is hard enough!"

The fixed value theories are discussed comparing the problem to Lamb shift (main topic in the 1947 Shelter Island conference). The author leads the reader through the Lamb shift in the presence of external gravitons discussion to short and long distance modifications to gravity. There is no solution visible in those directions.

In the adjustable scenario, several possibilities are mentioned: unimodular gravity, non-propagating four-form field strengths, scalar potentials with many minima, rolling scalar with nearly flat potential, spacetime wormholes, self-tuning, and explicit tuning (one or more free parameters). Among the mechanisms leading to the observed CC value the following are discussed: the Hartle-Hawking wavefunction favoring the smallest positive value of CC, the de Sitter entropy suggesting that the HH wavefunction has some statistical interpretation in terms of the system exploring all possible states, and the Coleman-de Lucchia amplitude for tunneling from positive to negative CC vanishing for some parameter range keeping the universe in the state of smallest positive energy density. Polchinski considers all these tantalizing in the same way as supersymmetry is as a solution for the CC problem. These mechanism would work in an empty universe. Next, I quote "In the course of trying to find selection mechanisms, one is struck by the fact that, while it is difficult to select for a single vacuum of small cosmological constant, it is extremely easy to identify mechanisms that will populate all possible vacua — either sequentially in time, as branches of the wavefunction of the universe, or as different patches in an enormous spatial volume. Indeed, this last mechanism is difficult to evade, if the many vacua are metastable: inflation and tunneling, two robust physical processes, will inevitably populate them all.

But this is all that is needed! Any observer in such a theory will see a cosmological constant that is unnaturally small; that is, it must be much smaller than the matter and energy densities over an extended period of the history of the universe. The existence of any complex structures requires that there be many ‘cycles’ and many ‘bits’: the lifetime of the universe must be large in units of the fundamental time scale, and there must be many degrees of freedom in interaction. A large negative cosmological constant forces the universe to collapse to too soon; a large positive cosmological constant causes all matter to disperse. This is of course the argument made precise by Weinberg, here in a rather minimal and prior-free form.

Thus we meet the anthropic principle. Of course, the anthropic principle is in some sense a tautology: we must live where we can live. There is no avoiding the fact that anthropic selection must operate. The real question is, is there any scientific reason to expect that some additional selection mechanism is operating?

If there is a selection mechanism, it must be rather special. It must evade the general difficulties outlined above, and it must select a value that is almost exactly the same as that selected by the anthropic principle, differing by one order of magnitude out of 120. Occam’s razor would suggest that two such mechanisms be replaced by one — the unavoidable, tautological, one. Thus, we should seriously consider the possibility that there is no other selection mechanism significantly constraining the cosmological constant. Equally, we should not stop searching for such a further principle, but I think one must admit that the strongest reason for expecting to find it is not a scientific argument but a psychological one: we wish fundamental theory to be as predictive as we have long assumed it would be."

That's correct, next comes a discussion of the string landscape. And a chapter "What is String Theory?" This is very interesting, of course. But the best I can do is to recommend everybody to read Polchinski's talk! Final quote from the end: "Let me close with a quotation from Dirac: One must be prepared to follow up the consequences of theory, and feel that one just has to accept the consequences no matter where they lead. And a paraphrase: One should take seriously all solutions of one’s equations. Of course, his issue was a factor of two, and ours is a factor of 10^500."